In order to receive a signal over one or more communication channels, it is often beneficial to determine an estimate of one or more properties of the communication channels. For example, in some cases, an estimation of the delay and attenuation of a communication channel may aid in reception of a signal over that channel. Recently, ultra-wide bandwidth technology has been proposed as a possible candidate for high-speed, short-range wireless communications, as described in a first reference by M. Z. Win and R. A. Scholtz, “Ultra-wide bandwidth time-hopping spread spectrum impulse radio for wireless multiple-access communications,” IEEE Trans. Commun., Vol. 48, pp. 679-691, April 2000 (hereinafter referred to as the first reference); a second reference by M. Z. Win and R. A. Scholtz, “Impulse radio: how it works,” IEEE Commun. Lett., vol. 2, pp. 36-38, February 1998 (hereinafter referred to as the second reference); and a third reference by S. Roy, J. R. Foerster, V. S. Somayazulu, and D. G. Leeper, “Ultrawideband radio design: the promise of high-speed, short-range wireless connectivity,” Proc. IEEE, vol. 92, pp. 295-311, February 2004 (hereinafter referred to as the third reference), which are hereby incorporated by reference in their entirety.
Much research has been conducted to derive receivers that fully explore the benefits of an UWB system, as described, for example, in J. D. Choi and W. E. Stark, “Performance of ultra-wideband communications with suboptimal receivers in multipath channels,” IEEE J. Select. Areas Commun., vol. 20, pp. 1754-1766, December 2002 (hereinafter referred to as the fourth reference), which is hereby incorporated by reference in its entirety. Among all the UWB receivers studied, the Rake receiver is considered to be a practically achievable structure with good performance, as described, for example, in G. L. Turin, “Introduction to spread-spectrum antimultipath techniques and their application to urban digital radio,” Proc. IEEE, vol. 68, pp. 328-353, March 1980 (hereinafter referred to as the fifth reference), which is hereby incorporated by reference in its entirety. In the Rake receiver, the received signal is often assumed to be a superposition of many delayed and attenuated copies of the transmitted signal. The rake receiver may use knowledge of the delays and the attenuations introduced by the UWB channel in order to perform coherent detection. As a result, estimating the channel delays and the channel attenuations before data recovery may be useful. As described in M. Z. Win and R. A. Scholtz, “Ort the energy capture of ultrawide bandwidth signals in dense multipath environments,” IEEE Commun. Lett., vol. 2, pp. 245-247, September 1998 (hereinafter referred to as the sixth reference), maximum likelihood (ML) estimators nor the UWB channel delays and the UWB channel attenuations have been proposed using unmodulated UWB signals. The estimators in the sixth reference require unmodulated signals and this is generally impractical for Rake receivers. As described in V. Lottici, A. D'Andrea, and U. Mengali, “Channel estimation for ultrawideband communications,” IEEE J. Select. Areas Commun., vol. 20, pp. 1638-1645, December 2002 (hereinafter referred to as the seventh reference), which is hereby incorporated by reference in its entirety, data-aided (DA) and non-data-aided (NDA) ML estimators for the delays and the attenuations in a UWB channel are obtained using time-hopped and pulse-position-modulated (TH-PPM) UWB signals. The data aided estimators in the seventh reference uses practical signals but also uses the transmission of overhead symbols. The non-data aided estimator in the seventh reference does not use overhead symbols but has poor performance.